72Morphology of polyhedral crystals

been confirmed that if the position of a quartz crystal with r z is reversed while growing in an autoclave, the crystal takes a form with r z, associated with the reversed partitioning of an Fe ion and the depth of the resultant purple color [14]. On inspection of the structural form, we see that the difference in the order of morphological importance is very small, and r is more important than z. This experiment demonstrates that the growth rate R of two faces whose morphological importance differs by very little can be reversed according to the flow of the solution over the faces, and also that the partitioning of the impurities is influenced to such an extent that it also can be reversed.

In natural crystals, whose growth processes cannot be directly observed, the difference in R is recorded as the difference in separation in growth banding (see Chapter 6). Based on these observations, several papers were reported in which the direction of flow of ore-forming fluid was evaluated in pegmatite and hydrothermal veins. In many cases in which the natural mineral crystals exhibited extensively malformed Habitus from that predicted by the structural form, the malformation could be considered to be due to the remarkable anisotropy involved in the environmental conditions, such as the directional flow of the solution, which is similar to the situation of growth of NaCl from solution in between two glass plates, as discussed above.

4.4.3 Whiskers

Crystals showing an extremely elongated form in one direction are called whiskers. Whiskers may appear in any type of crystal, irrespective of whether the structural form is predicted to be prismatic or cubic. Special attention was first paid to whiskers when it was demonstrated that Sn whiskers grown through the coating of electric wire have a plastic strength close to that of a perfect crystal. However, mineral crystals exhibiting whisker morphology were observed long before this, examples being jamesonite (Pb4FeSb6S14) and millerite (NiS). Hair silver, the name given to the elongated form of native Ag, is another example of a natural whisker. Various forms, such as coils (see Fig. 2.2(a)) and ropes, are also seen. Since whiskers have high plastic strength, they are often used as composite materials.

These remarkably elongated forms, which are not expected from the structure, have their origins in the strong anisotropy involved in either environmental conditions or in growth sites. Many models have been proposed as possible growth mechanisms of whiskers, but we refer to the following as a well established example.

When a solid particle of Au is placed on a Si substrate and SiI2 vapor is supplied in the heated system, whiskers of Si with Au droplets at the tips are formed. We know these are whiskers of Si, because only Si (S) grows in eutectic liquid droplets of Si–Au (L) formed by Au and Si supplied in the vapor phase (V). The Au–Si eutectic

4.4 Growth forms 73

liquid droplet provides the unique growth site. This mechanism is called the VLS (vapor–liquid–solid) mechanism [15]. The reason why only Si, and not Au, grows is due to thermodynamics, which states that the phase able to grow in a eutectic liquid is determined uniquely by the composition of the liquid phase. Si crystals take whisker forms as an inevitable result of the limited growth site within the liquid droplet. Various materials and systems other than Si have been known to form whiskers by the VLS mechanism. In all cases, a solidified liquid droplet is present at the tip of a whisker. The growth of the whiskers occurs at the roots.

If supersaturated NaCl (or KCl) aqueous solution is kept in a wineskin or cellophane bag in the shade, numerous NaCl (or KCl) whiskers grow on the surface of the wineskin after a few days. The explanation is that a supersaturated solution is transported by capillary action to the surface of the wineskin, which rapidly attains a highly supersaturated state, and crystallization starts. As a result, hollow tube whiskers are formed, and the supersaturated solution is transported to the tip of the whisker until the point at which the tube is closed, resulting in the formation of whiskers. There is only one growth site, and so this whisker grows at the tip [16].

The growth of Sn whiskers through the coating of electric wire occurs at the roots. Various models have been suggested to explain the mechanism of root growth of whiskers, VLS being one example. The following models also describe this growth:

(1)whiskers grow like toothpaste squeezed from a tube, because only one screw dislocation in a small crystallite acts as an active center for growth, and no growth takes place at grain boundaries, or

(2)one-directional growth results at a twin re-entrant corner (see Section 7.2) [17].

If an edge of a solid Ag2Te or Ag2Se crystal is pointed and electric current is allowed to pass through an electrode on the solid, whiskers of Ag start to grow from the pointed corner, since the Ag is supersaturated [18]. When the electric current is reversed, the Ag whisker is absorbed into the solid as the Ag in the solid becomes undersaturated. This is an example of root growth.

If screw dislocations outcropping on only one out of three crystallographically equivalent faces behave as active growth centers, whereas those on the other two faces are inactive for some reason, elongated whiskers will be formed in one direction. If screw dislocations on two faces are active as growth centers, a thin platy

Habitus will appear. Depending on the growth conditions, needles and thin platy KCl crystals can coexist with ordinary cubic crystals. However, this has still not clearly answered why some screw dislocations are active growth centers whereas others are inactive.

74 Morphology of polyhedral crystals

In a crystal bounded by F and S faces, a kinetic roughening transition occurs on the morphologically less important S face prior to on the F face. Kinetic roughening may occur by adsorption of impurity elements. In the case of oxide crystals, a de-oxidation process may be involved to retain electronic neutrality by adsorption of impurity ions with different charges. This is equivalent to the transformation of an S face into a K face by breaking the PBCs. On F faces containing more than two PBCs, impurity ions behave differently from those on S faces; a de-oxidation process is not involved, and so F faces behave as smooth interfaces, whereas S faces transform into K faces. Therefore, a prismatic crystal grows in one direction and takes a needle form. If we take the Berg effect into consideration, two-dimensional nucleation occurs more easily along the edges between K faces and F faces, which are rougher than at the center of the face, leading the growth in the prismatic direction. On the other hand, the growth of F faces is controlled by the layer growth mechanism, and the crystal protrudes along the edges of the K faces. This leads to the formation of hollowed whiskers. It has been shown that with increasing impurity content, the terminal faces (i.e the faces appearing on the tips of prismatic or needle crystals) of prismatic SnO2 and TiO2 crystals change from flat {111} to rounded faces, and further skeletal faces occur due to preferential nucleation along the edges, and eventually hollowed needle crystals appear [19]. Figure 4.9 shows a series of scanning electron microscope (SEM) photographs showing this change. If a similar roughening transition occurs only on the side faces of platy crystals, and if the basal plane behaves like a smooth interface, a thin platy crystal will be formed. Since roughening transitions occur under higher temperature and higher driving force, in addition to the effects of impurities it is anticipated that a malformed needle or thin platy Habitus will appear more frequently at higher temperatures and supersaturation conditions.

Crystals with a hollow tube prismatic form and their deviations (such as scrolls or ice cream cones) have been observed among clay minerals having a sheet structure and in fullerene, encouraging research into the origin of such unusual forms. Imogolite, a clay mineral, (OH)6Al4O6Si2(OH)2, occurs as a hollowed tube-like prismatic crystal; kaolin, Al2Si2O5(OH)4, takes the form of scrolled crystals; and chrysotile, which is formed by a hydrothermal treatment of serpentine, Mg3Si2O5(OH)4, looks like ice cream cones (Fig. 2.2 (b)) [20], [21]. Fullerene (C60 with a soccer ball form) exhibits a hollowed fibrous form called carbon nanotubes [22]. These nanotubes are of an appropriate diameter to accommodate metal atoms, and so efforts have been made to utilize them as potential materials for one-dimensional conductors or sensors.

It is not easy to provide an explanation of the origin of these unusual forms simply based on preferential growth at the tip of a prismatic crystal. Various models have been proposed, for example: